Cluster Self-Organization of Intermetallic Systems: K3, K4, and K6 Clusters-Precursors for the Self-Assembly of Li₂₈Cu₄Si₈-oP40, La₁₂Rh₁₂Al₁₆-oP40, and Ca₈Pt₁₂Sn₂₀-oP40 Crystal Structures

Abstract— Using computer methods (the ToposPro software package), a combinatorial-topological analysis and modeling of the self-assembly of Li₂₈Cu₄Si₈-oP40 (a = 7.969 Å, b = 4.449 Å, c = 17.244 Å, V = 611.46 ų), La₁₂Rh₁₂Al₁₆-oP40 (a = 26.949Å, b = 4.218Å, c = 7.267 Å, V = 826.05 ų), and Ca₈Pt₁₂Sn₂₀-oP40 (a = 27.701 Å, b = 4.614 Å, c = 9.371 Å, V = 1198.02 ų) crystalline structures with the Pnma space group are carried out. For Li₂₈Cu₄Si₈-oP40, the self-assembly of the crystal structure with the participation of supraclusters-trimers from K6(4a) = 0@6(Li₄Cu₂) clusters, two clusters K6(8d) = 0@6 (CuLi₅), and Si spacer atoms is considered. For La₁₂Rh₁₂Al₁₆-oP40, the self-assemblies of the crystal structure with the participation of K3(8d) = 0@3(LaRhAl) clusters and K6(4a) = 0@6(La₂Rh₂Al₂) clusters from the linked LaRhAl clusters and K4(8d) = 0@4(LaRhAl₂) clusters are considered. For Ca₈Pt₁₂Sn₂₀-oP40, the self-assembly of the crystal structure from clusters-precursors in the form of the K6 = 0@6(CaSn₃Pt₂) double tetrahedra and K4 = 0@4(CaSn₂Pt) tetrahedra is considered. The symmetry and topological code of the processes of the self-assembly of Li₂₈Cu₄Si₈-oP40, La₁₂Rh₁₂Al₁₆-oP40, and Ca₈Pt₁₂Sn₂₀-oP40 from K3, K4, and K6 clusters-precursors are reconstructed in the following form: primary chain → layer → framework.